The European Union and Britain on Friday tripped over the first item in their Brexit talks — protecting the rights of each other's citizens — highlighting the potential for trouble ahead in their marathon negotiations.

While British Prime Minister Theresa May declared that she had offered a "fair and serious" proposal on citizens' rights, European Union chief Donald Tusk dismissed it as falling "below our expectations." Dutch Prime Minister Mark Rutte said "thousands of questions" remained on the key topic.

The 27 EU leaders demanded many more details on the U.K. proposal to guarantee the rights of the 3 million EU citizens who now live in Britain.

Since many of those citizens will want to stay even as Britain itself leaves the EU, it is an immediate issue where May has a lot of leverage. The British leader is insisting that the EU needs to give the 1.5 million Britons living on the continent equal respect. She will outline a more detailed proposal next Monday, when May addresses her parliament in London.

Alongside citizens' rights, the Brexit negotiators will address the substantial bill that Britain will have to pay to quit the EU and the problems surrounding the border in Ireland.

"I want to reassure all those EU citizens who are in the U.K., who've made their lives and homes in the U.K., that no one will have to leave, we won't be seeing families split apart. This is a fair and serious offer," May said.

Yet many EU leaders were nonplussed by May's offer, saying there was a clear deal to leave such Brexit issues to the top negotiators, Michel Barnier for the EU and David Davis for Britain.

German Chancellor Angela Merkel said May's move was "not yet the breakthrough" that EU nations were looking for, adding "there is a long road in front of us."

Tusk agreed.

"My first impression is that the U.K.'s offer is below our expectations, and that it risks worsening the situation of citizens," Tusk said. "It will be for our negotiating team to analyze the offer line by line."

Exactly one year after British voters chose to leave the EU and after months of political chaos at home, a weakened May sent her team into the Brexit negotiations that began Monday. The issue of citizens' rights was seen as her strongest point to make an immediate impact.

May promised that the fate of EU citizens will be a priority in Brexit negotiations. She laid out benchmarks for their rights and said they should be shielded from excessive harm because of the political divorce.

Under May's proposal, EU citizens with legal residence in the U.K. will not be asked to leave and will be offered a chance to regularize their situation after Brexit. May also promised to cut the burdensome bureaucracy such paperwork can involve. EU citizens now face an imposing 85-page form to tackle if they want to stay.